Problem: $z=32+41.9i$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=41.9i$ and $\text{Im}(z)=32$ (Choice B) B $\text{Re}(z)=41.9$ and $\text{Im}(z)=32$ (Choice C) C $\text{Re}(z)=32$ and $\text{Im}(z)=41.9$ (Choice D) D $\text{Re}(z)=32$ and $\text{Im}(z)=41.9i$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={32}+{41.9}i$ is of the form ${a}+{b}i$, where ${a}={32}$ and ${b}={41.9}$. Therefore: $\text{Re}(z)={a}={32}$. $\text{Im}(z)={b}={41.9}$. Summary $\text{Re}(z)={32}$ and $\text{Im}(z)={41.9}$.